@misc{Baczyński_Michał_Krzysztof._Autor_Properties_2014,
 author={Baczyński, Michał Krzysztof. Autor and Grzegorzewski, Przemysław Wojciech. Autor and Helbin, Piotr. Autor and Niemyska, Wanda Helena. Autor},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2014},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={Recently, Grzegorzewski [5, 6, 8] introduced two new families of fuzzy implication functions called proba­bilistic implications and probabilistic S-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In the same article [8] author gives a motivation to his idea and indicates some interesting connections between new families of implications and the dependence structure of the underlying environment. In this paper the laws of contraposition, the law of importation and T-conditionality are studied for these families of fuzzy implications. Furthermore, we discuss intersections of both new families of implications with R-implications, SN-implications and QL-operations.},
 type={Text},
 title={Properties of the Probabilistic Implications and S-Implications},
 keywords={Copulas, Kopuły, Fuzzy implications, Probabilistic implications, Laws of contraposition, Law of importation, Functional equations, Implikacje rozmyte, Implikacje probabilistyczne, Prawa transpozycji, Prawo importu, Równania funkcyjne, T-conditionality, T-uwarunkowanie},
}